Add your hashtag and IFTTT will keep track of tweets from it
If
New tweet from search
This Trigger fires every time a new tweet matches your search query. Limited to 30 tweets per check, and protected tweets will not be returned.
Then
Add row to spreadsheet
This action will add a single row to the bottom of the first worksheet of a spreadsheet you specify. Note: a new spreadsheet is created after 2000 rows.
Explore more great ways to automate Google Sheets and Twitter